Conventional RAIM algorithms may be based on either a weighted or un-weighted least squares solution where the errors in each satellite's pseudo-range measurement are uncorrelated with the errors in the other satellites' pseudo-range measurements.
However, the ionospheric error (which can be the dominant error source) in each satellite's pseudo-range is, in fact, highly correlated with that of each of the other satellites. By ignoring this correlation, the computed Horizontal Protection Limit (HPL) which bounds the horizontal position error is much larger than necessary. As a result the availability of GPS to do a low Required Navigation Performance (RNP) approach suffers.